Padé approximations of exponential (phi) functions
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Exponential functions, in a general sense, are defined as
E_j(x) = ∑_k x^k/(k+j)!
So for j=0, this is the regular exponential.
The main application is to apply that exponential function to a matrix.
Here is a minimal example:
from padexp import Exponential import numpy as np e = Exponential(4) # to compute the functions E_j for 0 ≤ j ≤ 4 M = np.array([[1.,2.],[3.,4]]) e(M) # returns a list containing [E_0(M), E_1(M),...,E_4(M)]
This code is useful for exponential integrators, and is a port of the expint Matlab package.